NOT EVEN WRONG tells a fascinating and complex story about human beings and their attempts to come to grips with perhaps the most intellectually demanding puzzle of all: how does the universe work at its most fundamental level?

The story begins with an historical survey of the experimental and theoretical developments that led to the creation of the phenomenally successful '' of particle around 1975. But, despite its successes, the Standard Model left a number of key questions unanswered and therefore continued in their attempt to find a powerful, all-encompassing theory.

Now, more than twenty years after coming onto the scene, and despite a total lack of any success in going beyond the Standard Model, it is that dominates . How this extraordinary situation has come about is a central concern of this book.

As explains, the term 'superstring theory' really refers not to a well-defined theory, but to unrealised hopes that one might exist. As a result, this is a 'theory' that makes no predictions, not even wrong ones, and this very lack of falsifiability has allowed it not only to survive but to flourish.

The absence of experimental evidence is at the core of this controversial situation in physics - a situation made worse by a refusal to challenge conventional thinking and an unwillingness to evaluate honestly the arguments both for and against theory. To date, only the arguments of the theory's advocates have received much publicity. NOT EVEN WRONG will provide readers with another side of this story, allowing them to decide for themselves where the truths of the matter may lie and to follow an important and compelling story as it continues to unfold. \ NOT EVEN WRONG IS AN AUTHORITATIVE AND WELL REASONED ACCOUNT OF 'S EXTREMELY FASHIONABLE STATUS AMONG TODAY'S THEORETICAL PHYSICISTS. THE HOLD THAT STRING THEORY HAS, WORLD­ PETER WOIT is a and mathematician. WIDE, ON TODAY'S CUTTING-EDGE RESEARCH INTO THE FUNDAMENTAL He graduated in 1979 from with LAWS OF THE UNIVERSE IS VERY REMARKABLE, CONSIDERING THE LACK OF bachelor's and master's degrees in physics and went ANY OBSERVATIONAL SUPPORT FOR THIS BODY OF IDEAS. WOIT SUPPLIES on to be awarded his PhD in from . He was a postdoc at the Institute THE FIRST THOROUGH AND DETAILED ANALYSIS AIMED AT EXPLAINING THIS for Theoretical Physics at Stony Brook and at the EXTRAORDINARY PHENOMENON. I FOUND IT COMPULSIVE READING, AND Mathematical Research Institute at Berkeley. I REGARD IT AS AN IMPORTANT BOOK.' He is now a lecturer in the mathematics department , AUTHOR OF THE ROAD TO REALITY at , , where he has been since 1989, recently teaching graduate courses in THIS IS A COURAGEOUS AND NECESSARY BOOK THAT SHOULD SPARK A quantum theory, representation theory, and . DEBATE ABOUT THE FUTURE OF THEORETICAL PHYSICS.' , AUTHOR OF THE LIFE OF THE COSMOS

POPULAR '

ISBN 0-224-07605-1 JONATHAN CAPE JACKET: AN ARTISTICALLY ENHANCED PICTURE OF RANDOM HOUSE PARTICLE TRACKS IN THE BEBC, BIG EUROPEAN BUBBLE CHAMBER. (COURTESY: CERN) 20 VAUXHALL BRIDGE ROAD 9 '7 8 0 2 2 4"0 760 50 I OMnOM SW1V 9<5A Not Even Wrong

The Failure of String Theory and the Continuing Challenge to Unify the Laws of Physics

Peter Woit

JONATHAN CAPE LONDON Published by Jonathan Cape 2006

2468 10 9 75 3 1

Copyright © Peter Woit 2006

Peter Woit has asserted his right under the Copyright, Designs and Patents Act 1988 to be identified as the author of this work

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First published in Great Britain in 2006 by JONATHAN CAPE Random House, 20 Vauxhall Bridge Road, London SW1V 2SA

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Typeset by Palimpsest Book Production Limited, Polmont, Stirlingshire Printed and bound in Great Britain by William Clowes Ltd, Beccles, Suffolk For Ellen Contents

Acknowledgements xi Introduction 1 About this book 8

1. Particle Physics at the Turn of the Millennium 10 2. The Instruments of Production 14 Basic principles 14 Experimental particle physics, a quick history 18 Current accelerators 28 Accelerators: future prospects 31 Further reading 36 3. Quantum Theory 38 Quantum theory and its history 39 Further reading 56 4. 58 Further reading 66 5. Gauge Symmetry and Gauge Theories 67 Further reading 74 6. The Standard Model 75

vii Not Even Wrong

The standard model: electro-weak interactions 76 The standard model: strong interactions 83 Further reading 91 7. Triumph of the Standard Model 92 Further reading 97 8. Problems of the Standard Model 98 9. Beyond the Standard Model 102 Grand unified theories 102 Technicolour 104 and 107 10. New Insights in Quantum Field Theory and Mathematics 113 113 in Yang-Mills theory and in mathematics 116 Lattice 120 Large N 122 Two-dimensional quantum field theories 124 Anomalies and quantum mechanical 129 Topological quantum field theory 132 Further reading 145 11. String Theory: History 146 S- 146 The first string theories 153 The first superstring theory revolution 156 The second superstring theory revolution 161 Recent trends 163 Further reading 166 12. String Theory and Supersymmetry: An Evaluation 167 Supersymmetry 168 Superstring theory 179 String theory, supersymmetry and mathematics 193

viii Contents

13. On Beauty and Difficulty 198 14. Is Superstring Theory Science? 208 15. The 217 16. The Only Game in Town: The Power and the Glory of String Theory 224 17. The Landscape of String Theory 240 18. Other Points of View 250 19. Conclusion 258

Notes 268 Index 275

ix Acknowledgements

y knowledge about the topics discussed in this book is the prod­ Muct of many years spent in both the mathematics and physics communities, and I've benefited over this time from conversations on these topics with a large number of mathematicians and physicists. By now this number is so large that I'm afraid I'm only able to remem­ ber and thank those who have been of help during the last few years while I've been writing this book and seeing it through to publication. Of important assistance have been string theorists and other string- friendly physicists who have been willing to share their expertise with me as part of discussions about string theory in various inter­ net venues. I've learned a great deal from these discussions, so even though many of them are not likely to be very happy with this book, their efforts have made it a much better one than would otherwise have been possible. For help of this kind, I'd like specifically to thank Aaron Bergman, Sean Carroll, Jacques Distler, Robert Helling, Clifford V. Johnson, Lubos Motl, Moshe Rozali and Urs Schreiber. During the past few years I've been grateful to the many people who have contacted me, sometimes anonymously, with expressions of support and enthusiasm, often together with an interesting story of one sort or another. Finding out that my concerns about the present state of particle theory are so widely shared has been an important incentive for the writing of this book.

xi Not Even Wrong I'd also like to thank Roger Astley of Cambridge University Press, together with Jim Lepowsky and several anonymous referees. While publication by Cambridge ultimately didn't work out, going through the process there ultimately turned the original manuscript into a much better book. At a later stage, Binky Urban provided excellent advice about what should be done to make the book a success, much of which I fear I haven't taken. Professor Karl von Meyenn provided me with the reference indi­ cating that the attribution of the phrase 'Not Even Wrong' to Pauli is not as apocryphal as I had feared, together with useful comments about the context of the phrase and the influence of the Vienna Circle on Pauli's thinking. John Horgan has provided encouragement and advice, together with interesting discussion of his views on some of the topics treated here. Among friends and supporters who have listened to me go on far too long about string theory and some of the other subjects treated here, I'd like especially to thank Oisin McGuinness, Nathan Myhrvold, Peter Orland and Eric Weinstein, as well as my Columbia colleagues Bob Friedman, John Morgan, D.H. Phong and Michael Thaddeus, whose interest and support have been invaluable. It has been an honour to have the opportunity to discuss in person or via e-mail some of the issues treated here with some truly great mathematicians and physicists, all of whom have provided helpful advice. These include Gerard 't Hooft, Lee Smolin and Martin Veltman, as well as two people whose work has had an overwhelmingly large influence on my understanding of mathematics and physics, Sir Michael Atiyah and Edward Witten. While many of them may disagree very strongly with the point of view from which I am writing, whatever value there is in it owes a lot to them. Another great physicist, Sir Roger Penrose, was of critical help in encouraging this project and helping to find it a publisher, for which I am exceedingly grateful. My editors at Jonathan Cape, Will Sulkin and Richard Lawrence, have been a pleasure to work with and I hope they won't regret their willingness to help me write and publish exactly the book I've wanted

xii Acknowledgements to write, one that may be more intellectually uncompromising than most publishers would find comfortable. Finally, I owe an immeasurable debt to Ellen Handy. Her exten­ sive editorial assistance over many years has created a text of far higher quality than would otherwise have been conceivable. More importantly, her love, selfless encouragement and unwavering belief in me have made possible the writing of this book, and much else besides.

xiii Introduction

he impulse to speculate about the of the physical world Tof which we are all somehow a part is a characteristic trait of human beings. As a socially organised activity, such speculation has an extremely long history and has achieved truly dramatic successes during the past century. Theoretical physics is the speculative activ­ ity that asks the most fundamental questions about physical reality, and it has found beautiful and persuasive answers to many of these questions. These answers turn out to be most naturally expressed not in natural language, but in the language of mathematics. The power and sophistication of mathematical language has grown tremendously in recent centuries, often in tandem with the struggle to find answers to questions raised by physicists. The story of how the discovery of the principles of special rela­ tivity and revolutionised twentieth-century physics is by now a rather old one. By 1973, physicists had in place what was to become a fantastically successful theory of fundamen­ tal particles and their interactions, a theory that was soon to acquire the name of the 'standard model'. Since that time, the overwhelm- ing triumph of the standard model has been matched by a similarly overwhelming failure to find any way to make further progress on fundamental questions. How has this situation come about and what are the prospects of it ever changing?

1 Not Even Wrong

This book is an attempt to come to terms with this question from a very particular point of view. This point of view is a little bit unusual, so I'll begin with some personal history. My earliest memories of being concerned with the issues to be discussed in this book go back to the first years of the 1970s, to hours spent poring over every book about astronomy I could find in the local public library. At some point I came across the subject of ; in particular that part of the subject that studies the structure of stars by writing down and then solving equations for the temperature, pressure and composi­ tion of the interior of a star. That one could hope to understand in such a detailed and precise way exactly what was going on in the unimaginable interior of a star fascinated me, but was also mystify­ ing. The equations in the books I was reading were expressed in a mathematical language I could not understand, and were derived from physical laws about which I knew nothing. I began trying to study the necessary mathematics and physics to make sense of these equations. As I learned some basic ideas about calculus and elementary physics, one of the first striking lessons was that mathematics and physics were intertwined in a very complex way. Mechanics, the part of elementary physics that deals with the motions of particles and the forces that cause these motions, is based upon Newton's laws, which require calculus for their expression. Newton had developed calculus and mechanics at the same time and the two subjects are so completely entangled that one cannot understand one properly without understanding the other. Using the language of calculus, Newton's laws are exceedingly simple and clear statements about the way that at least part of the world works. As I took more physics books out of the library, I began to find out about other areas of physics than mechanics, and soon came across and fell in love with something that has fascinated me to this day: quantum mechanics. While the equations of Newton's refer to easily visualisable quantities such as the position and velocity of particles, the fundamental equation of quantum mechanics, Schroedinger's equation, concerns a mathematical entity completely out of the realm of ordinary experience, the wave- function. While the wave-function and Schroedinger's equation for it

2 Introduction seem to have no relation to anything one can visualise, they have allowed physicists to understand and predict precisely an incredible variety of physical phenomena that take place on the distance scale of the size of an individual atom. One book that made a strong impression on me was 's memoir Across the Frontiers,1 in which he tells the story of his experiences during the 1920s, the early days of quantum mechanics. He describes long debates with his friends about the nature of physical reality, held during hikes in the local mountains. The basic ideas at issue were those that soon led him, Erwin Schroedinger and others to the explosion of new ideas about physics that was the birth of quantum mechanics in 1925. Later on, after I had learned more about events in Germany between the wars, the image of Heisenberg and others in his youth group marching around the mountains to attend large inspirational gatherings began to take on more troubling aspects. Part of the appeal of quantum mechanics to me was its peculiar character of being a kind of esoteric practice. Through long study and deep thought, one could hope to arrive at an understanding of the hidden nature of the universe. Unlike other popular exotic reli­ gious or mind-altering activities of the time, this sort of search for enlightenment appeared to be both much more solid and something for which I actually had some talent. When I went off to college at Harvard in 1975, I soon found that the physics department there was in a state of great excitement, in some ways similar to that which had characterised physics soon after the birth of quantum mechanics fifty years earlier. The standard model had recently been formulated, and experimental evidence for it was beginning to pour in. This theory was a quantum field theory, a more sophisticated version of the quantum mechanics I was just beginning to study seriously. My undergraduate adviser was Sheldon Glashow, and in the office two doors down was , with whom he would later share a for their independ­ ent work on part of the standard model. One of the young postdocs was David Politzer, a co-discoverer of the other main piece of the theory. He would soon be joined by another postdoc, Edward Witten from Princeton, who was destined to be the next leader of the field.

3 Not Even Wrong Great things had happened and more were expected imminently from this impressive array of talent. During my college years I spent a formative summer working on a particle physics experiment at the Stanford Linear Accelerator Center, and a lot of time trying to figure out what quantum field theory was all about. I graduated in 1979 with a hazy idea of the subject and some basic notions about the standard model, and went on directly to doctoral study at Princeton. The physics department faculty there included who, with his student , had played a crucial role in the development of the stan­ dard model. It was soon to include Witten, who returned to Princeton as a tenured professor directly from his postdoc, skipping over the usual tenure track. For me, this was a time of seriously getting down to learning quantum field theory, and beginning to try to do some original work. For the field as a whole, it was the beginning of a frus­ trating period. Many ideas were floating around about how to go beyond the standard model, but none of them seemed to be work­ ing out successfully. I left Princeton in 1984 to spend three years as a postdoctoral research associate at the Institute for Theoretical Physics at SUNY Stony Brook. My arrival there coincided with a period that came to be known as the 'First Superstring Revolution', a series of events that will be described later in this book, and which marked a great change in the field of particle theory. By the last of my three years at Stony Brook, it became clear to me that someone interested in mathemat­ ics and quantum field theory wouldn't have much of an immediate future in a physics department unless he or she wanted to work on the new superstring theory. This impression was confirmed by the negative results of a job search for a second postdoc. Since my research interests involved the parts of quantum field theory closest to mathematics and I did not want to do superstring theory, it seemed that it would be a good idea to try my luck look­ ing for employment among the mathematicians. I moved back to Cambridge, where the physics department at Harvard let me use a desk as an unpaid visitor, and the mathematics department at Tufts hired me as an adjunct to teach calculus. From there I went on to a one-year postdoctoral research associate position at the Mathematical

4 Introduction Sciences Research Institute at Berkeley, followed by a four-year non­ tenure track junior faculty appointment in the mathematics depart­ ment at Columbia. This change of fields from physics to mathematics turned out to be a wise move, and I have now been at Columbia in the maths department for more than sixteen years. Currently, I'm happily in the non-tenured but permanent faculty position of 'Lecturer', with one of my main responsibilities being to make sure that the department's computer system keeps functioning properly. I also teach classes at the undergraduate and graduate level, as well as continuing to do research in the area of the mathematics of quantum field theory. My academic career path has been rather unusual and I'm very much aware that it has been based on a significant amount of good luck. This began with the good fortune of having parents who could afford to send me to Harvard. It continued with being in the right place at the right time to take advantage of an uncommon opportu­ nity to work in an excellent maths department surrounded by talented and supportive colleagues. The experience of moving from physics to mathematics was some­ what reminiscent of a move in my childhood from the to France. Mathematics and physics each have their own distinct and incompatible languages. They often end up discussing the same thing in mutually incomprehensible terms. The differences between the two fields are deeper than simply that of language, involving very distinct histories, cultures, traditions and modes of thought. Just as in my childhood, I found that there is a lot to learn when one makes such a move, but one ends up with an interesting bi-cultural point of view. I hope to be able to explain some of what I have learned about the complex, continually evolving relationship between the subjects of physics and mathematics and their corresponding academic cultures. When I left physics in 1987, the subject of superstring theory had taken over most of the attention of leading theoretical physicists. As far as I could tell, it did not seem like a very promising idea, and was destined to go the way of many other failed ideas of the period. What neither I nor anyone else knew at the time was that more than twenty years after coming onto the scene, despite the lack of any success

5 Not Even Wrong whatsoever at going beyond the standard model, superstring theory would still continue to dominate particle theory. How this peculiar situation has come about is one of the central concerns of this book. Many books about physics written for a non-specialist audience are inspirational narratives of progress and triumph. Several recent popular books about superstring theory fit into this mould. This book is of a different nature, telling a story about a scientific field that, while it has experienced great success, as a result has fallen on hard times, in many ways a victim of that same success. I believe this is an interesting and important story that needs to be told, albeit in many ways not at all an inspirational one. The physicist was, with Heisenberg, Schroedinger and Dirac, one of the early leaders in the development of quantum mechanics. He was renowned for being a tough audience, exclaim­ ing 'wrong' (falsch), or 'completely wrong' (ganz falsch) when he disagreed with a speaker. Near the end of his life, when asked his opinion of a recent article by a younger physicist, he sadly said 'it is not even wrong' (Das ist nicht einmalfalsch).2 This story has circulated widely among physicists, often in different versions, and the term 'not even wrong' has sometimes come to be used as a general term of abuse for completely silly ideas. It is likely that Pauli, who was heavily influenced by the positivistic philosophy of science of the Vienna Circle, had in mind a more specific sort of criticism. A scien­ tific idea is 'not even wrong' if it is so incomplete that it cannot be used to make predictions that could be compared to observations to see if the idea is wrong. In 1984, relatively little was known about superstring theory. A vast amount of research work since then has made it clear that Pauli's phrase is now an accurate description of the status of the theory and several physicists have publicly characterised it as such.3 As we will see, the term 'superstring theory' really refers not to a well-defined theory, but to unrealised hopes that one might exist. As a result, this is a 'theory' that makes no predictions, not even wrong ones, and this very lack of falsifiability is what has allowed the whole subject to survive and flourish. This situation raises important issues that we will examine. Is a subject a science if it makes no predictions at all? When is very speculative research part of science and when is it not?

6 Introduction What happens when speculation not subject to the discipline of experiment completely takes over a scientific field? When I sat down to write about some of these topics, I began by trying to write out a short history of quantum mechanics and particle theory. My perspective was different from that of most exercises of this kind, which typically ignore the role of mathematics in this story. As I looked more deeply into some of the standard books on the subject, I noticed something intriguing. One of the major figures in the small circle of people who discovered and developed quantum theory was actually a mathematician, Hermann Weyl. During the very short period during which physicists were working out quantum mechanics in 1925 and 1926, Weyl was in constant communication with them, but was himself in a burst of inspiration doing the purely mathematical work that was to be the high point of his career. The field of mathematics Weyl was involved with at the time is known as group representation theory, and he was well aware that it was the right tool for understanding part of the new quantum mechanics. Physicists were almost entirely baffled by Weyl's mathematics and how it fitted into the new quantum theory, even after Weyl quickly wrote a book containing alternate chapters on quantum theory and representation theory.4 For many years the book was considered a classic, but most physicists probably read just half of the chapters. Group representation theory is the mathematical expression of the notion of a 'symmetry', and understanding of the importance of this notion slowly grew among particle theorists throughout the 1950s and 1960s. By the 1970s, courses on group representation theory involving parts of Weyl's work had become a standard part of the theoretical physics curriculum. From then on, particle theory and mathematics have interacted closely in a very complex way. Explaining the twists and turns of this story is one of the main goals of this book. The positive argument of this book will be that historically one of the main sources of progress in particle theory has been the discov­ ery of new symmetry groups of nature, together with new represen­ tations of these groups. The failure of the superstring theory programme can be traced back to its lack of any fundamental new symmetry principle. Without unexpected experimental data, new

7 Not Even Wrong theoretical advances are only likely to come about if theorists turn their attention away from this failed programme and towards the diffi­ cult task of better understanding the symmetries of the natural world.

About this book

This book attempts to tell a complicated story that may be of inter­ est to readers with a wide range of different backgrounds. Some parts of the story are inescapably rather technical, involving not very widely known parts of both mathematics and physics. As a result, most read­ ers are likely to have trouble with at least some chapters. The more technical chapters have been written without the use of equations, and an attempt has been made as much as possible both to avoid technical vocabulary and to offer at least some sort of explanation of vocabulary that can't be avoided. These choices lead to a certain lack of precision that experts may find trying. While the hope is that many non-experts will be able to follow much of these chapters, the large number of difficult and abstract concepts involved are likely to make this quite a challenge. Such chapters have been structured to begin with an introductory section summarising in general terms what is at issue and how it fits into the story of the book. Professional physicists and mathemati­ cians are quite used to the idea that one cannot hope always to follow a technical discussion and one needs to be ready to skip ahead to where things again get less demanding. Just about all readers should find this tactic necessary at one point or another. For those who want truly to understand some of the more technical chapters, a section at the end of these chapters gives an annotated list for suggested further reading. A real understanding of many of the topics discussed can't be achieved by reading a few pages of text, but requires travelling a rather difficult path. I hope at least to describe the land­ marks on that path and point readers to where such a journey really begins, should they choose to embark on it. Much of this book is about history, and an accurate description of this history, were it possible, would require a very different and much larger volume. What appears here is more of a quick sketch, ignoring

8 Introduction the fine details of exactly who discovered what, when. In place of this there is often just a short description of the physicists or math­ ematicians whose names have conventionally been attached to vari­ ous discoveries. This by no means should be taken to indicate that these are necessarily the actual discoverers. In a course on particle physics which I took at Harvard, given by the Spanish physicist Alvaro De Rujula, I learnt that whenever he introduced a concept with someone's name attached to it, he would generally say something like the following: 'This is the so-called Weinberg angle, which of course was discovered not by Weinberg, but by Glashow.' On one occasion, after introducing a named concept, he stopped for a while and seemed to be thinking deeply. Finally he announced that, as far as he knew, strangely enough, this concept actually seemed to have been discovered by the person whose name was attached to it. Much of the story I am telling is uncontroversial and most experts on the subject would more or less agree with how it is being told here. On the other hand, the reader should be aware that later parts of this book are about topics that are quite controversial and my point of view on these topics is by no means a majority one. Readers will have to judge for themselves how much credence to give to my argu­ ments, and this is one reason for including here both some unusu­ ally technical material as well as a fair amount of detail about the background and experiences of the author. From my earliest interest in science, one of the most appealing aspects for me was that it involved a notion of truth not based on appeal to authority. Judgements about scientific truth are supposed to be based on the logical consistency of arguments and the evidence of experiment, not on the eminence of those claiming to know the truth. The absence of this experimental evidence is at the source of the controversial situation in physics that will be examined here, but things have been made much worse by groupthink, a refusal to chal­ lenge conventional thinking, and an unwillingness to evaluate honestly the arguments for and against string theory. To date, only the arguments from enthusiasts for the theory have received much publicity. This book will provide readers with another side of this story; they will then be in a position to evaluate for themselves where the truths of the matter may lie.

9 1 Particle Physics at the Turn of the Millennium

t the end of his closing talk at a conference in Kyoto in 2003, A the theoretical physicist David Gross finished with a dramatic flourish, quoting from a speech of Winston Churchill's. In Gross's version, near the end of his life Churchill rose to give a campaign speech: 'Never, never, never, never, never give up.' This story is similar to one repeated by many people, but the real source of Gross's quote is a speech Churchill gave at Harrow school during the war, which contains the lines:

this is the lesson: never give in, never give in, never, never, never, never - in nothing, great or small, large or petty - never give in except to convictions of honour and good sense.

The conference was entitled 'Strings 2003' and it brought together several hundred theoretical physicists who work on 'string theory', a set of ideas that has dominated theoretical particle physics for the last two decades. Gross is one of the world's most prominent theo­ rists; after a very distinguished career at Harvard and Princeton, he is now director of the Kavli Institute for Theoretical Physics at Santa Barbara. He was to share the 2004 for work done in 1973 that was of huge significance for the field of particle physics. What had disturbed Gross so much that he would invoke

10 Particle Physics at the Turn of the Millennium the words Churchill used to rally his country during the dark days of the Nazi bombardment of London? His concern was that recent developments in string theory may be leading many physicists to abandon the traditional central goal of theoretical physics: to understand the physical world in terms of a simple compelling theory, and use this to make predictions that test this understanding. Gross quoted from a section of Einstein's auto­ biographical writings, written late in his life at the age of sixty-seven:

... I would like to state a theorem which at present can not be based upon anything more than upon a faith in the simplicity, i.e. intelligi­ bility, of nature:... nature is so constituted that it is possible logically to lay down such strongly determined laws that within these laws only rationally completely determined constants occur (not constants, there­ fore, whose numerical value could be changed without destroying the theory) ...1

Einstein is stating the creed that Gross and most theoretical physi­ cists believe: there is a single set of simple underlying laws that describe how the universe works, and these laws are uniquely deter­ mined. There are no extra parameters that determine the theory; once one gets the right idea about what the laws are, there are no additional numbers that one needs to specify to write them down. Gross's Nobel prize was awarded for his 1973 co-discovery of an extremely successful theory of one of the forces experienced by certain kinds of elementary particles, and this theory has exactly the uniqueness property that Einstein believed in. This theory has no free parameters that can be adjusted to fit experiment, and yet it accurately predicts a wide range of different experimental results. The abandonment of Einstein's creed that so worried Gross has taken the form of an announcement by several leading theorists that string theory is compatible with an unimaginably large number of different possible descriptions of the world and, as a result, perhaps the only predictions it can make are those that follow from the 'anthropic principle'. The anthropic principle is essentially the idea that our very existence puts constraints on what physical laws are possible. These must be such that intelligent beings such as ourselves

11 Not Even Wrong

could somehow evolve. If a huge number of different universes exist, all with different physical laws, we are guaranteed to be in one of the ones where intelligent life is possible. One of the leading proponents of this point of view is Leonard Susskind, a professor at Stanford and one of the co-discoverers of string theory, who explains:

Mostly physicists have hated the idea of the anthropic principle; they all hoped that the constants of nature could be derived from the beau­ tiful symmetry of some mathematical theory . . . Physicists always wanted to believe that the answer was unique. Somehow there was something very special about the answer, but the myth of uniqueness is one that I think is a fool's errand ... If there were some fundamen­ tal equation which, when you solved it, said that the world is exactly the way we see it, then it would be the same everywhere. On the other hand you could have a theory which permitted many different environments, and a theory which permitted many different environ­ ments would be one in which you would expect that it would vary from place to place. What we've discovered in the last several years is that string theory has an incredible diversity - a tremendous number of solutions - and allows different kinds of environments. A lot of the practitioners of this kind of mathematical theory have been in a state of denial about it. They didn't want to recognize it. They want to believe the universe is an elegant universe - and it's not so elegant. It's different over here, it's that over here. It's a Rube Goldberg machine over here. And this has created a sort of sense of denial about the facts about the theory. The theory is going to win, and physicists who are trying to deny what is going on are going to lose .. 2

Susskind's vision of the universe as a complicated, inelegant Rube Goldberg machine that is the way it is because of the necessity of supporting life has gained an increasing number of adherents, and he has written a popular book on the subject entitled The Cosmic Landscape: String Theory and the Illusion of ? Gross refers to the anthropic point of view as a 'virus'4 that has infected many physicists, who show no signs of ever recovering from the disease. He tells the story of his younger colleague Joe Polchinski at

12 Particle Physics at the Turn of the Millennium Santa Barbara, who at one point felt that anthropic reasoning was so nefarious he would resign his professorship rather than engage in it, but now has gone over to the other side. Two years after Strings 2003, in a public talk, at Strings 2005 in Toronto, Susskind was describ­ ing the ongoing controversy as a 'war' between two groups of physi­ cists, also comparing it to a 'high-school cafeteria food fight'. He claimed that his side was winning, with Gross's in retreat, and accused his opponents of being in 'psychological denial' and engaged in 'faith- based science'. At a panel discussion held during the Toronto confer­ ence, the panel of leaders in the field split evenly over the anthropic issue, while the audience voted 4 or 5 to 1 against Susskind's point of view. How did particle physics get itself into its current state, in which some of its most prominent practitioners question whether their colleagues have given up on science? Have they? Why has there been so little progress in this subject for the last quarter-century, and where should one look for ways to change this situation? The following chapters will describe some of the history that has led particle physics to its current predicament. Since 1973, the field has failed to make significant progress, and in many ways has been the victim of its own success. The reasons for this failure will be examined, and an attempt will also be made to extract lessons from the history of previous successes that may indicate a more promising way forward.

13 2 The Instruments of Production

The bourgeoisie cannot exist without constantly revolutionizing the instruments of production . . . Karl Marx, The Communist Manifesto1

he central concern of this book is the recent history and Tpresent state of theoretical particle physics, especially in its relationship to mathematics, but to understand anything about this, one has first to understand the material conditions which are funda­ mental to particle physics research. Particle accelerators and detectors are the 'instruments of production' used to create the base of experimental data upon which all theorising about elementary particles is built. The continuing improvement and refinement of these experimental tools is what has driven progress in particle theory during much of the past century. This chapter will explain the basic principles governing how accelerators work, describe some of their history and present state, and finally consider what the prospects are for their future.

Basic principles

Before it is possible to explain any of the basic physical principles needed to understand how experimental particle physics is done, certain fundamental conventions of how to describe measurements have to be set. This is the question of what system of measurement units to use. There are many different possible choices of units in

14 The Instruments of Production use in different subfields of physics, but particle physicists have one preferred set of units, sometimes referred to as 'God-given' or 'natu­ ral' units. These units are chosen so as to take advantage of basic features of special relativity and quantum mechanics, getting rid as much as possible of constants that depend on choice of measure­ ment units by choosing such units so that these constants are set equal to one. A fundamental postulate of special relativity is that space and time are linked together so that the speed of is always constant, no matter in which reference frame it is measured. This is what makes the subject paradoxical from the point of view of everyday experi­ ence: if I try to move at high speed in the same direction as a beam of light, no matter how fast I go, the light will always be moving away from me at the same speed. The equations of special relativ­ ity simplify when units of measurement for space and time are chosen to be such that the speed of light is equal to one. For example, one way of doing this is to note that light travels 300,000 kilometres in a second, so it travels about a foot in a nanosecond (the prefix 'nano' means 'one billionth'). As a result, measuring lengths in feet and times in nanoseconds would make the speed of light about one. Setting the speed of light equal to one determines the choice of units used to measure time in terms of the choice of units used to meas­ ure space, and vice versa. Perhaps the most famous equation related to Einstein's special relativity is the E = mc2 equation relating energy (E), (m) and the speed of light (c). Note that using units in which the speed of light 'c' is set equal to one simplifies this to E = m, so energy and mass become equal in the context described by this equation. As a result, particle physicists use the same units to measure energy and mass. While special relativity links together the way spatial dimensions and the time dimension are measured, quantum mechanics links together energy and time measurements. This will be explained in greater detail later on, but two basic facts about quantum mechan­ ics are that: 1. There is a mathematical entity called a 'state-vector' that describes the state of the universe at a given time.

15 Not Even Wrong 2. Besides the state-vector, the other fundamental mathematical entity of the theory is called the Hamiltonian. This is an operator on state-vectors, meaning that it transforms a given state-vector into a new one. Operating on a general state-vector at a given time, it tells one how the state-vector will change during an infinitesimal additional time period. In addition, if the state-vector corresponds to a state of the universe with a well-defined energy, the Hamiltonian tells one what this energy is. The fact that the Hamiltonian simultaneously describes the energy of a state-vector, as well as how fast the state-vector is changing with time, implies that the units in which one measures energy and the units in which one measures time are linked together. If one changes one's unit of time from seconds to half-seconds, the rate of change of the state-vector will double and so will the energy. The constant that relates time units and energy units is called Planck's constant (after the physicist ) and conventionally denoted with the letter 'h'. It is generally agreed that Planck made an unfortunate choice of how to define the new constant he needed since it almost always comes into equations divided by a factor of two times the mathematical constant pi (3.14159 . . .). As a result, physicists prefer to work with Planck's constant h divided by two times pi, a constant conventionally written as an h with a bar through it and called h-bar. Particle physicists choose their units so as to make h-bar equal to one and this fixes the units of time in terms of the units of energy, or vice versa. With these choices of the speed of light and h-bar, distance units are related to time units, and time units are related to energy units, which in turn, as described before, are related to mass units. The standard convention of particle physics is to express everything in energy units, and thus one just has to pick a single measurement unit, that which determines how energies are expressed. Here, the­ orists bow to the experimentalists, who long ago found it most convenient to measure energies in electron-volts. An electron-volt (abbreviated eV) is the energy an electron picks up as it moves between two metal plates that have a voltage difference of one volt between them. Once one has chosen to measure energies and in units of eV, then the choice of constants described earlier means

16 The Instruments of Production that time and space (which are measured in inverse units to energy) are measured in 'inverse electron-volts' or (eV)-1. To get a feel for what these energy units are like, the following table gives the values of various masses and energies corresponding to several different particle physics phenomena (some to be described in more detail later on), all in electron volts. The standard abbrevi­ ations for large numbers of electron-volts include: 103 eV = 1 keV (kilo electron-volt), 106 eV = 1 MeV (Mega electron-volt), 109 eV = 1 GeV (Giga electron-volt), 1012 eV = 1 TeV (Tera electron-volt).

Energy Example

0.04 eV Energy of atoms in air at room temperature 1.8-3.1 eV Energy of photons of visible light 100-100 000 eV X-rays 20 keV Kinetic energy of electrons in a television monitor More than 100 keV Gamma-rays 511 keV Mass of electron 1-10 MeV Energies produced in nuclear decays 105 MeV Mass of muon 938 MeV Mass of proton 93 GeV Mass of Z 1 TeV Energy in each proton in a beam at the Tevatron

All the energies in this table are those of a single particle or photon, so on everyday scales they are very small amounts of energy, with 1 TeV being about the same as the kinetic energy (energy of motion) of a slow-moving ant. There is a much larger energy that theorists sometimes consider, the 'Planck energy' of about 1019 GeV. This is conjecturally the energy scale at which quantum effects of gravity become important. It is a much more significant amount of energy, corresponding roughly to the chemical energy in a car's tank of petrol. In the units we are discussing, the unit of distance is the inverse electron-volt, which in more conventional units would be about a

17 Not Even Wrong micron (10-6 metres, a millionth of a metre). Time is also measured in inverse electron-volts and this unit of time is extremely short, roughly 4 x 10-15 seconds. Since energies are measured in eV and distance in (eV)-1, particle physicists tend to think of distances and energies interchangeably, with one being the inverse of the other. The energy corresponding to the mass of a proton is 1 GeV, a billion electron-volts. Since this energy is a billion times larger than an elec­ tron-volt, the corresponding distance will be one billion times smaller or 10-9 x 10-6 = 10-15 metres. One can think of this distance as being the characteristic size of the proton. Particle physicists equivalently refer to their investigations as involving either very short distance scales or very high energy scales. Typical physical processes under study involve something that happens at some particular approximate distance or approximate energy, and this is said to be the distance or energy 'scale' under study. In accelerators the total energy of the particles one is collid­ ing together sets the energy scale one can study. Investigating shorter and shorter distances requires higher and higher energies and at any given time the fundamental limit on the experimental information one can gather about elementary particles comes from the techno­ logical limits on the energies of particles in one's experiments.

Experimental particle physics, a quick history

The history of experimental particle physics is by now a quite long and complex one; this section will give a quick sketch of some of this history. The fundamental experimental technique of particle physics is to bring two particles close together and then watch what happens. The simplest way to do this is to begin by in one way or another producing a beam of energetic particles, and then accelerating the particles to high energy in some sort of accelerator. The beam of high-energy particles is then aimed at a fixed target, and one uses a detector of some sort to see what particles come out of the region where the beam hits the target. A simple example of this concept is behind the design of a tele­ vision set. In a cathode ray tube television design, a beam of elec-

18 The Instruments of Production trons (the 'cathode rays') is accelerated by high voltages, towards a target which is the back of the screen of the television. Magnetic fields are used to control the beam, in which the electrons reach energies of about 20,000 electron-volts. When the beam hits the screen, collisions of the electrons with atoms in the screen produce reactions which lead to the emission of photons of light, which are then detected by the eyes of the television viewer watching the front of the screen. So the television is an accelerator with an electron beam and the detector which analyses the results of the collisions with the target (the screen) is the human eye. The kind of collisions going on in the television screen causes changes in the energy levels of the atoms in the screen, and as a result a television might be useful for studying the physics of atoms. If one is interested in even smaller scales or higher energies, a tele­ vision is not of any use, since the electron beam does not have enough energy to disrupt the atom and get at more fundamental physics. To see what happens when electrons collide not with the atom as a whole, but with its constituents (the nucleus and the electrons bound to the nucleus), much higher energies than those in a cathode ray tube are needed. During the past century many different p